Need MORE help on my tub drain please

Thanks to those who posted replies. Let me preface my dilemma by mentioning that my house was built in 1961 on a slab. Ouch, never again. 1st time homeowner and didn't know any better.

At any rate. I still believe I have some kind of mechanical blockage. I went and got the snake machine today and ran it as far as I could go until the bends beneath the tub stopped me, and I retrieved zero hair.

Again, our drain worked fine and quickly two days ago, then bang, completely stand still water. The face plate and stopper came out in one nice piece. This just doesn't make since to me. I think I may have to bite the bullet and call the plumber.

May I suggest one of the best drain cleaners that I've ever tried...DrainCare (tub or anything else). It's an enzyme-based (non-caustic) drain cleaner that eats out all organic matter overnight.
You just run warm water in the drain, pour the DrainCare in, and let it dissolve the hair, soap scum, body oils, etc. out. Then rinse it down the next morning with the hottest water that you can pour and run down it.
It has always worked for me. If the clog is really bad, then you may have to use it again, but it WILL work.
Good Luck!
Mike